Experimental and theoretical study of the optical frequency combs generated by gain-switching of semiconductor lasers

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(1)UNIVERSIDAD POLITÉCNICA DE MADRID. ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE TELECOMUNICACIÓN. TESIS DOCTORAL. EXPERIMENTAL AND THEORETICAL STUDY OF THE OPTICAL FREQUENCY COMBS GENERATED BY GAINSWITCHING OF SEMICONDUCTOR LASERS. Alejandro Rosado Pérez Graduado en Física. Master Universitario en Materiales Avanzados. 2019.

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(3) UNIVERSIDAD POLITÉCNICA DE MADRID Centro de Materiales y Dispositivos Avanzados para las TIC Departamento de Ingeniería Fotónica y Bioingeniería Escuela Técnica Superior de Ingenieros de Telecomunicación. EXPERIMENTAL AND THEORETICAL STUDY OF THE OPTICAL FREQUENCY COMBS GENERATED BY GAINSWITCHING OF SEMICONDUCTOR LASERS. AUTOR: Alejandro Rosado Pérez Graduado en Física. Master Universitario en Materiales Avanzados. DIRECTORES: Ignacio Esquivias Moscardó Dr. Ingeniero de Telecomunicación José Manuel García Tijero Dr. en Ciencias Físicas 2019.

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(5) Resumen El trabajo de investigación realizado en el marco de esta tesis doctoral se ha centrado en la generación de Peines Ópticos de Frecuencia (OFC) en láseres de semiconductor mediante la técnica de conmutación de ganancia (GS). El trabajo ha sido fundamentalmente experimental, si bien se han empleado simulaciones para contribuir a una mejor comprensión de la fı́sica interna del proceso de generación de OFCs. Se han empleado diversos tipos de láser, fundamentalmente láseres de realimentación distribuida (DFB) y láseres de modo discreto (DML). Se ha realizado una caracterización experimental exhaustiva de las propiedades de los OFCs generados mediante GS en un rango completo de condiciones de operación a distintas frecuencias de repetición, tanto en el rango de los GHz, con aplicaciones en comunicaciones ópticas, como en el rango de las centenas de MHz, de aplicación en espectroscopı́a. En el estudio experimental se ha investigado el efecto de la inyección óptica sobre las propiedades de los OFCs, obteniéndose interesantes resultados, como la mejora o empeoramiento de la calidad de los espectros en función de las condiciones de conmutación y de inyección. Se han encontrado las condiciones óptimas de operación para generar OFC de alta calidad a las distintas frecuencias consideradas. Con el fin de mejorar la comprensión de los diferentes procesos fı́sicos involucrados en la generación de los OFCs por conmutación de ganancia, se ha desarrollado una herramienta de simulación basada en el modelo de ecuaciones de balance para láseres de semiconductor, con especial consideración en el tratamiento de las fuentes de ruido. Para una correcta simulación de los OFCs se requiere el conocimiento de un conjunto de parámetros internos de los láseres; que se obtuvieron mediante un procedimiento original basado en la medida de los espectros del Ruido Relativo de Intensidad (RIN). Mediante este procedimiento se ha reducido la incertidumbre en los resultados simulados, al ser posible extraer mayor número de parámetros que mediante otros procedimientos gracias a un adecuado tratamiento analı́tico de las ecuaciones del RIN. Las simulaciones han reproducido por completo la respuesta temporal y espectral de diferentes láseres en un rango amplio de condiciones eléctricas y de inyección óptica. A partir de las simulaciones se han comprendido los procesos fı́sicos predominantes que contribuyen a la generación de OFCs, “chirp” dinámico a altas frecuencias de repetición, y “chirp” adiabático a bajas frecuencias. Se ha demostrado que es posible mejorar las caracterı́sticas de los OFCs a baja frecuencia mediante el empleo de excitación con pulsos eléctricos, en lugar de las habituales señales sinusoidales. Se han generado OFCs de alta calidad a 100 MHz (hasta 866 tonos en 10 dB) con buena relación portadora a ruido. También se ha demostrado que es posible emplear “Step-recovery diodes” (SRDs) como fuente de pulsos eléctricos para generar OFCs, reduciendo el costo y tamaño de los equipos involucrados, y manteniendo buena calidad en las caracterı́sticas de los OFCs. El papel del “jitter” de la fuente eléctrica en la calidad de los OFCs ha sido estudiado teórica y experimentalmente. i.

(6) Finalmente, los OFCs generados mediante conmutación de ganancia e inyección óptica han sido empleados para medir los espectros de absorción de diferentes elementos, utilizando tres arquitecturas diferentes. Se ha empleado detección heterodina, espectroscopı́a de peine dual, y se ha implementado por primera vez la técnica de peine dual con un único láser por conmutación de la frecuencia de GS. Los resultados han sido prometedores de cara a la aplicación de estos OFCs en espectroscopı́a de gases.. ii.

(7) Abstract The research work carried out within the framework of this PhD has focused on the generation of Optical Frequency Combs (OFC) in semiconductor lasers using the gainswitching (GS) technique. The work has been mainly experimental, although simulations have been used to contribute to a better understanding of the internal physics of the OFCs generation process. Various types of lasers have been used, specially distributed feedback (DFB) lasers and discrete mode lasers (DML). An exhaustive experimental characterisation of the properties of the OFCs generated by GS in a full range of operating conditions has been performed. Two ranges of repetition frequencies have been explored: the GHz range with applications in optical communications, and the range of hundreds of MHz for application in spectroscopy. The effect of the optical injection (OI) on the properties of the OFCs has been investigated, and interesting results have been obtained, such as the improvement or deterioration of the quality of the spectra depending on the GS and OI conditions. The optimal operating conditions to generate high quality OFCs at the different frequencies considered have been found. In order to improve the understanding of the different physical processes involved in the generation of the OFCs generated by GS, a simulation tool based on the rate equation model for semiconductor lasers has been developed, with detailed treatment of the noise sources. For a correct simulation of the OFCs the values of a set of internal laser parameters is are required. They were obtained through an original procedure based on the measurement of the relative intensity noise (RIN) spectra. Using this procedure, the uncertainty in the simulated results has been reduced, since it allows to extract more parameters than other procedures due to an adequate analytical treatment of the RIN equations. The simulations have completely reproduced the temporal and spectral response of different lasers in a wide range of electrical and optical injection conditions. From the simulations, the predominant physical processes that contribute to the generation of OFCs, dynamic ”chirp” at high repetition frequencies, and adiabatic ”chirp” at low frequencies, have been identified. It has been shown that it is possible to improve the characteristics of low frequency OFCs by driving the laser with electric pulses, instead of using sinusoidal driving. High quality 100 MHz OFCs (up to 866 tones in 10 dB) with good carrier-to-noise (CNR) ratio have been generated. It has also been shown that step-recovery diodes (SRDs) can be used as a source of electrical pulses to generate OFCs, thus reducing the cost and size of the equipment involved, while maintaining the quality of the OFCs. The role of the “jitter” of the electrical source in the quality of the OFCs has been studied theoretically and experimentally. Finally, the OFCs generated by gain-switching and optical injection have been used to measure the absorption spectra of different elements, using three different architectures: heterodyne detection, and dual-comb spectroscopy and a new implementation of iii.

(8) this technique. In this implementation the dual-comb is generated from a single GS laser by alternating the repetition frequency. Promising results for the application of these OFCs in gas spectroscopy have been obtained.. iv.

(9) Agradecimientos Esta tesis es el resultado de 3 años de esfuerzo conjunto del grupo de investigación al que pertenezco, y en particular, de mis directores de tesis Ignacio y José Manuel. Sin su paciencia y esfuerzo, hoy yo no podrı́a estar escribiendo esta tesis. Jamás podré expresar con palabras la gratitud que siento por haberme enseñado tantı́simo durante estos años. Agradecer también a la financiación de este grupo de investigación durante los años de desarrollo de esta tesis, en particular, al Ministerio de Economı́a y Competitividad de España a través de los programas COMBINA (TEC2015-65212-C3-2-P) y LIDERA (RTI2018-094118-B-C21) y a la Comunidad de Madrid por medio de los programas Sinfoton (SINFOTON-CM, S2013/MIT-2790) y Sinfoton 2 (SINFOTON2-CM, S2018/NMT4326). Poder contar con financiación durante la realización de la tesis ha sido una tremenda suerte, considerando los tiempos que corren. Al igual que con mis tutores, querı́a agradecer a todos los miembros del grupo de Fotónica Aplicada (GFA), Centro de Materiales y Dispositivos Avanzados para Tecnologı́as de Información y Comunicación (CEMDATIC) y a mis compañeros del Departamento de Fotónica y Bioingenierı́a de la ETSIT-UPM, de los cuales, me gustarı́a remarcar la labor particular de uno de ellos, Toni. Gracias por enseñarme tanto, por las discusiones cientı́ficas (y no tan cientı́ficas), y por tu buena disposición. Las cosas habrı́an sido muy diferentes sin tu ayuda, y quizás esta tesis hoy no estarı́a escrita sin ti. Tampoco quiero olvidar a Edu, Clara y David, mis compañeros de despacho durante toda esta aventura. Ası́ mismo, esta investigación tampoco habrı́a sido posible sin los profesores Ángel Valle y Luis Pesquera del Instituto de Fı́sica de Cantabria. Sin sus consejos, motivación, y sin lugar a duda, sin su BOSA, igual hoy no sabrı́amos tanto sobre peines de frecuencia. El tiempo que he pasado en Santander no habrı́a sido tan fructı́fero si no hubiera sido por vosotros. De igual manera, querı́a agradecer el trato y los consejos de la profesora Julia Arias durante mi estancia en Elche. Also, this thesis could have not been possible without Dr. Prince Anandarajah and Dr. Eamonn Martin, with whom I could work with during my internship in Dublin. Specially, I would like to thank both for your advises (not only scientific) and the way that you have treated me there. I will not forget it. Mas allá de la comunidad cientı́fica, esta tesis no habrı́a sido posible sin el apoyo y el cariño de las personas que me rodean, mis amigos y familia. Gracias a los que se fueron, y a los que se quedaron. También a la gran familia que he encontrado en los últimos dos años (”la de los palitos”), y en particular, a mis compañeros de clan (de los dos). Vuestro apoyo nunca caerá en saco roto. One name, one sky. Agradecer a los Gómez (y agregados) por todo el cariño y atención durante los últimos meses, y en particular, a mi compañera Sandra por su comprensión, ayuda y cariño. Por ultimo, pero no menos importante, a mi familia. Jamás podré expresar con palabras la gratitud, cariño y amor incondicional que siento por vosotros. Sin vosotros, hoy no serı́a quien soy ni estarı́a donde estoy.. v.

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(11) Contents 1 Introduction. 1. 1.1. Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 1.2. Objectives of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. 1.3. Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2 Fundamentals 2.1. 5. Semiconductor lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5. 2.1.1. Basic structure: Fabry-Perot laser . . . . . . . . . . . . . . . . . . .. 5. 2.1.2. Single frequency semiconductor lasers . . . . . . . . . . . . . . . . .. 7. 2.2. Gain-switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. 2.3. Optical injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13. 2.4. Optical frequency combs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. 2.5. 2.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. 2.4.2. Comb operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15. 2.4.3. OFC generation from semiconductor lasers . . . . . . . . . . . . . . 16. Homodyne and heterodyne detection . . . . . . . . . . . . . . . . . . . . . . 20. 3 Dynamic response of a semiconductor laser. 25. 3.1. Rate equation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25. 3.2. Noise treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30. 3.3. Numerical algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31. 3.4. Dimensionless model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. 4 Experimental techniques. 35. 4.1. Laser devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35. 4.2. CW measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37. 4.3. Impedance measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39. 4.4. Gain-switching and optical injection . . . . . . . . . . . . . . . . . . . . . . 40. 4.5. Temporal and spectral characterisation . . . . . . . . . . . . . . . . . . . . . 41. 4.6. Dual-comb spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 vii.

(12) 5 Optical pulse and frequency comb generation in gain-switched semiconductor lasers. 47. 5.1. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47. 5.2. OFC generation in 1550 nm DML and DFB lasers . . . . . . . . . . . . . . 49. 5.3. 5.2.1. CW characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 49. 5.2.2. OFC generation by gain-switching . . . . . . . . . . . . . . . . . . . 50. 5.2.3. OFC generation by gain-switching with optical injection . . . . . . . 54. Optical pulse generation in gain-switched 1300 nm VCSELs . . . . . . . . . 58 5.3.1. CW characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 58. 5.3.2. Optical pulse generation by gain-switching . . . . . . . . . . . . . . . 60. 6 Numerical and experimental analysis of optical frequency comb generation. 65. 6.1. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65. 6.2. Analytical expression for the RIN spectrum . . . . . . . . . . . . . . . . . . 66. 6.3. Parameter extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70. 6.4. Comparison between experiments and simulations. . . . . . . . . . . . . . . 74. 6.4.1. OFC generation by gain-switching without optical injection . . . . . 74. 6.4.2. OFC generation by gain-switching with optical injection . . . . . . . 81. 7 OFC generation by pulsed gain-switching and optical injection. 87. 7.1. State of the Art and rationale . . . . . . . . . . . . . . . . . . . . . . . . . . 87. 7.2. OFC generation with a pulse pattern generator . . . . . . . . . . . . . . . . 89. 7.3. OFC generation using step-recovery diodes . . . . . . . . . . . . . . . . . . 96. 8 Spectroscopic applications of optical frequency combs. 101. 8.1. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101. 8.2. Heterodyne spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102. 8.3. Dual-comb spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106. 8.4. Gated dual-comb generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 8.4.1. Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . 110. 8.4.2. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. 9 Conclusions and future work. 115. Bibliography. 120. List of acronyms. 136. viii.

(13) List of Figures 2.1 2.2 2.3. 2.4 2.5. 2.6 2.7 2.8 2.9 2.10 2.11 2.12. 2.13 2.14 2.15. 2.16. (a) Schematics of a FP laser diode. (b) Band diagram of the conduction and valence bands in a single quantum-well laser . . . . . . . . . . . . . . Schematics of a FP cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Measured power-current curve of a commercial discrete mode laser (Ith = 14.5 mA). More details about the experimental device are provided in Chapter 4. (b) Gain spectra and cavity losses together with the wavelengths of the longitudinal modes of the cavity (extracted from [1]) . . . . . . . . Measured optical spectrum of a commercial FP laser (Roithner LFO-18-ip) at I = 45 mA (Ith = 8 mA). This figure was extracted from [1] . . . . . . (a) Schematic of a Bragg grating structure: a periodic array of alternating regions with different indices n1 and n2 with a period Λ; (b) Reflected power as a function of β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic of a DBR laser . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Schematic of a DFB laser; (b) Measured optical spectrum of a DFB at Ibias = 25 mA. More details of this laser are provided in Chapter 4. . . . . Schematic view of the DML structure. Top: SEM image of the etched feature pattern. Figure extracted from [2] . . . . . . . . . . . . . . . . . . Measured optical spectrum of a DML at Ibias = 25 mA. More details of this laser are provided in Chapter 4. . . . . . . . . . . . . . . . . . . . . . . . . Schematic representation of a VCSEL . . . . . . . . . . . . . . . . . . . . (a) Measured optical spectrum of a 1300 nm VCSEL. Panel (b) is a zoom of (a). More details of this device can be found in Chapter 4. . . . . . . . (a) Result of simulations of the current (black), carrier density (red) and photon density (blue) during the turn-on process; (b) Enlarged view during the first spike of the relaxation oscillations . . . . . . . . . . . . . . . . . . Results of simulations at 5 GHz of the current (black), carrier density (red) and photon density (blue) in GS operation . . . . . . . . . . . . . . . . . . Schematics of the configuration for the OI of a laser diode: ML: master laser, SL: slave laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Measured RF spectra of the delayed self-heterodyne signal of a DFB laser for Ibias = 30 mA without (blue) and with OI (red). More details are provided in Chapter 5. (b) Simulated RIN spectra for Ibias = 20 mA without (blue) and with OI (red); external light is injected with Pinj = 12 dBm and δν = 5.4 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . Train of optical pulses and the corresponding OFC . . . . . . . . . . . . .. ix. . .. 6 6. .. 7. .. 8. . .. 8 9. .. 9. . 10 . 10 . 11 . 11. . 12 . 13 . 13. . 14 . 16.

(14) 2.17 Schematic diagram of mode-locking principle: (a) each longitudinal mode oscillates without phase correlation; (b) The phase of each mode is locked, i.e, mode-locked operation. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.18 Schematic diagram of electro-optic modulation technique for OFC generation, LD: laser diode, EOM: electro-optic modulator . . . . . . . . . . . . 2.19 (a) Experimental train of pulses from a DML driven at fR = 5 GHz, Ibias = 30 mA and VRF = 1; (b) The corresponding optical spectrum in the same driving conditions. More information about this spectrum is provided in Chapter 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.20 Experimental train of pulses from a GS-DFB: (a) No injection; (b) With OI. This figure is extracted from [3]. . . . . . . . . . . . . . . . . . . . . . 2.21 Optical spectra of a gain-switched DFB laser (a) without external injection and (b) with external injection. This figure was extracted from [3]. . . . 2.22 Left: Schematic diagram of the DSH technique: LD: laser diode, PD: photodiode, ESA: electrical spectrum analyser. Right: Fundamental of the DSH technique, reproduced from [4]. . . . . . . . . . . . . . . . . . . . . . . . . 2.23 Left: Schematic diagram of the dual-comb fundamentals, based on [5]. . . 2.24 Three different dual-comb architectures: (a) Free-running; (b) Mutuallycoherent; (c) Fully referenced. This figure has been extracted from [5]. . . 2.25 (a) Schematic diagram of the dual-comb spectroscopy; (b) Different configurations in dual-comb spectroscopy: (upper row) asymmetric configuration and (lower row) symmetric configuration. This figure has been extracted from [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 4.2. 4.3. 4.4. 4.5. 4.6. 4.7. . 17 . 18. . 18 . 19 . 19. . 21 . 21 . 22. . 23. Photograph of the employed lasers: (a) VCSEL. (b) DFB laser and (c) DML. (a) Experimental setup for the measurement of the P-I-V characteristics; LD: laser diode, PD: photodetector, OI: optical isolator, EM: electrometer; (b) Example of an experimental P-I and V-I characteristics: in blue P-I, in red V-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Experimental setup for the acquisition of the optical spectra; LD: laser diode; OSA: optical spectrum analyser, OI: optical isolator; (b) Optical spectrum of the DFB at Ibias = 50 mA recorded with OSA . . . . . . . . . (a) Experimental setup for the measurement of the RF spectra; LD: laser diode; OSA: optical spectrum analyser, OI: optical isolator, PD: photodetector, ESA: electrical spectrum analyser; (b) RF spectrum of the VCSEL at Ibias = 4 mA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Experimental setup for the measurement of the linewidth: OS: optical source, AOM: acousto-optic modulator, PD: photodetector, ESA: electrical spectrum analyser (b) Measured spectrum of the DFB at Ibias = 30 mA and fitting with a Voigt profile . . . . . . . . . . . . . . . . . . . . . . . . . (a) Experimental setup for the measurement of the laser scattering parameters, LD: laser diode, PD: photodetector, OI: optical isolator. (b) Measured impedance of the DML at Ibias = 35 mA. . . . . . . . . . . . . . . . . . . . Schematics of a bias-tee . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. x. 36. 37. 38. 38. 39. 40 40.

(15) 4.8. 4.9. 4.10 4.11. 4.12. 4.13. 5.1. 5.2. 5.3. 5.4. Experimental setup for OI using the master-slave configuration, ML: master laser, SL: slave laser, VOA: variable optical attenuator, OSA: optical spectra analyser; PC: polarisation controller . . . . . . . . . . . . . . . . . . . . . (a) Schematics of the experimental setup for the temporal and spectral characterisation; LD: laser driver, DUT: device under test, PD: photodetector, OSC: oscilloscope, HR-OSA: high-resolution optical spectrum analyser, OI: optical isolator (b) Schematics of the experimental setup for the temporal and spectral characterisation including OI. . . . . . . . . . . . . . . . . . . Example of a temporal profile (a) and optical spectrum (b) for the DML in GS conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Temporal trace of the optical pulse of the VCSEL (Ibias = 4.5 mA, fR = 2 GHz and PRF = 16 dBm). (b) Spectrum of an OFC measured with the OSA (blue) and with the BOSA (red) (Ibias = 30 mA, fR = 5 GHz and VRF = 0.4 V). The arrows indicate the 10 dB spectral width (∆f10 = 20 GHz). (c) Closer look at the 1550.4 nm region of the spectrum. In (b), the carrier-to-noise ratio (CNR = 53 dB) is indicated. . . . . . . . . . . . . . Experimental setup with the symmetrical configuration for the dual-comb architecture: (a) With the AOM and (b) With the OBPF. ML: master laser, SL: slave laser (1&2), PC: polarisation controller, AOM: acousto-optic modulator, DUT: device under test, PD: photodetector, ESA: electrical spectrum analyser, OSC: oscilloscope, OBPF: optical bandpass filter . . . Experimental setup for the gated dual-comb architecture: ML: master laser, SL: slave laser, PC: polarisation controller, AOM: acousto-optic modulator, VOA: variable optical attenuator, PD: photodetector, ESA: electrical spectrum analyser, OSC: oscilloscope, EDFA: erbium doped fiber amplifier . . Left: P-I (in blue) and V-I characteristics at 25o C for the DML (a) and DFB laser (c); Right: Optical spectra at Ibias = 20 mA for the DML (b) and DFB laser (d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DFB Optical spectra for (a) different values of heat-sink temperatures: T = 15o C (in blue), T = 24o C (in red), T = 33o C (in black); and (b) different values of Ibias : 40 mA (in blue), 50 mA (in red), 60 mA (in black). DML Optical spectra for (c) different values of heat-sink temperatures: T = 15o C (in blue), T = 24o C (in red), T = 33o C (in black); and (d) different values of Ibias : 40 mA (in blue), 50 mA (in red), 60 mA (in black). . . . . . . . . Temporal traces (upper row) and optical spectra (lower row) of the DML emission at Ibias = 50 mA and fR = 500 MHz and different values of VRF . Each column corresponds to the value of VRF labelled on the top. . . . . . Evolution of the temporal traces (upper row) and optical spectra (lower row) of the DML with the modulation amplitude VRF for Ibias = 30 mA and fR = 5 GHz. Each column corresponds to the value of the VRF labelled on the top. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xi. . 42. . 42 . 43. . 43. . 44. . 45. . 50. . 51. . 52. . 52.

(16) 5.5. 5.6. 5.7. 5.8. 5.9. 5.10 5.11. 5.12. 5.13. 5.14. 5.15. 5.16. Evolution of CNR and ∆f10 as a function of the modulation amplitude VRF for the DFB laser (upper row) and the DML (lower row) at fR = 500 MHz (first and third columns) and fR = 5 GHz (second and fourth columns) for different bias currents. The stars indicate the best comb at each bias current. Temporal traces (upper row) and optical spectra (lower row) ot the gainswitched DFB laser (Ibias = 25 mA, fR = 5 GHz and VRF = 1.8 V) under several power levels of OI at δν of 6 GHz. The injection frequency is indicated with an arrow. The frequencies of the spectra are relative to the emission frequency of the free-running SL in CW operation. . . . . . . . . . Optical spectra of the gain-switched DFB laser (Ibias = 15 mA, fR = 5 GHz and VRF = 1.6 V) under OI (Pinj =-24 dBm) at several δν. The arrow indicate the frequency of the injection relative to the emission of the free-running SL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical spectra of the gain-switched DFB laser (Ibias = 25 mA, fR = 5 GHz and VRF = 1 V), under several power levels of OI at δν = 5 GHz. The arrows indicates the injection frequency relative to the SL emission in CW operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RF spectra of the DSH signal of the DFB laser with and without OI, (a) CW lineshape for Ibias = 30 mA. (b) Lineshape of the 1st tone of the OFC (Ibias = 30 mA, VRF = 1 V, fr = 5 GHz). (c) Linewidths of the first 5 tones of the OFC. For all panels, without OI is indicated in blue and with OI in red (Pinj = 6 dBm, δν = −1 GHz). . . . . . . . . . . . . . . . . . . . (a) P-I (in blue) and V-I (in red) characteristics of the VCSEL at 25o C; (b) VCSEL Optical spectrum at CW operation at Ibias = 3 mA. . . . . . . . . Schematic diagram of the experimental setup for the polarisation splitting; VCSEL: vertical-cavity surface-emitting laser, PC: polarisation controller, RP: rotable polariser, OSA: optical spectrum analyser . . . . . . . . . . . . (a) VCSEL Experimental optical spectra at 6 mA for the three different polarisations. (b) Closer look at the 1312.6 nm region of the spectra. Each polarisation is labelled in the legend of both figures. . . . . . . . . . . . . . VCSEL Optical spectra for (a) different values of Ibias (blue: 3 mA, red: 6 mA, black: 9 mA) and (b) different values of heat-sink temperature(blue: 20o C, red: 25o C, black: 30o C) . . . . . . . . . . . . . . . . . . . . . . . . . . Temporal traces (upper row) and optical spectra (lower row) of the VCSEL emission at PRF = 18 dBm and fR = 2.5 GHz and different values of Ibias . Each column corresponds to the value of Ibias labelled on the top . . . . . Temporal traces (upper row) and optical spectra (lower row) of the VCSEL emission at Ibias = 5 mA and fR = 2.5 GHz and different values of PRF . Each column corresponds to the value of PRF labelled on the top . . . . . . Evolution of Pmax (left) and the FWHM of the optical pulses of the optical pulses (right, in blue); and the corresponding value of 10-dB spectral width of the optical spectra (right, in red) generated in the VCSEL at fR = 2.5 GHz: (a) and (b) PRF = 18 dBm and Ibias variable; (c) and (d) Ibias = 5 mA and PRF variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xii. 54. 55. 56. 56. 57 58. 58. 59. 59. 60. 61. 62.

(17) 6.1. Semi-logarithmic plots of the RF spectra of the DML at Ibias = 20 mA (a) ”as recorded” and (b) after processing according to Eq. (6.34) . . . . . . . . 6.2 Semi-logarithmic plots of the RIN spectra of the DML at different values of Ibias ; (a) Ibias = 20 mA, (b) Ibias = 24 mA, (c) Ibias = 28 mA. Blue: experimental measurements. Red Lines: fits of measured RIN spectra to Eq. (6.24). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Parameters extracted from the fit of the RIN expression to the measured 0 spectra for the DML: (a) wr2 (blue squares) and 1/A (red squares) vs Ibias − Ith ; (b) γ vs wr2 ; (c) ωs2 vs wr2 . The lines correspond to numerical fits. . . . 6.4 RIN spectra of the DML for different values of Ibias ; (a) Ibias = 20 mA, (b) Ibias = 24 mA and (c) Ibias = 28 mA. Blue: experimental measurements, black line: simulations. (See text for details) . . . . . . . . . . . . . . . . . 6.5 Experimental (left) and simulated (right) optical spectra of the gain-switched DML laser at Ibias = 34 mA, fR = 5 GHz, and two values of VRF (top row VRF = 1 V, bottom row VRF = 1.8 V). . . . . . . . . . . . . . . . . . . . . . 6.6 Colour maps with the dependence on VRF and Ibias of the experimental (left) and simulated (right) spectral characteristics for fR = 5 GHz: (a) and (b), CNR; (c) and (d), ∆f10 ; and (e) and (f), CNR·∆f10 . . . . . . . . . 6.7 Temporal profiles at the same GS conditions as in Fig. 6.5 (Ibias = 34 mA, fR = 5 GHz and VRF = 1 V (left) and 1.8 V (right)): (a) and (b), experimental power; (c) and (d), simulated power (black) and chirp (orange); (e) and (f), simulated carrier density (black) and calculated threshold carrier density (orange); and (g) and (h), simulated current (black) and threshold current (orange) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8 Experimental (left) and simulated (right) optical spectra at Ibias = 60 mA, fR = 200 MHz and VRF = 1.5 V. . . . . . . . . . . . . . . . . . . . . . . . . 6.9 Colour maps with the dependence on VRF and Ibias of the experimental (left) and simulated (right) spectral characteristics for fR = 200 MHz: (a) and (b), CNR; (c) and (d), ∆f10 ; and (e) and (f), CNR·∆f10 . . . . . . . . . 6.10 Temporal profiles for Ibias = 60 mA, fR = 200 MHz and VRF = 1.5 V: (a) simulated current (black) and threshold current (orange); (b) simulated carrier density (black) and calculated threshold carrier density (orange) and (c) simulated output power (black) and chirp (orange). . . . . . . . . . . . . 6.11 Experimental (left column) and simulated (right column) optical spectra with OI for fixed GS conditions (Ibias = 32 mA, fR = 5 GHz and VRF = 1.8 V), using different values of Pinj and δν, (a) and (b), Pinj = 0 dBm and δν = 2 GHz, (c) and (d), Pinj = -36 dBm and δν = 2 GHz, (e) and (f), Pinj = 0 dBm and δν = - 66 GHz. The arrow indicates the injection frequency. 6.12 Colour maps with the dependence on Pinj and δν of the experimental (left) and simulated (right) of: (a) and (b) CNR , (c) and (d) δf10 , and (e) and (f) CNR·∆f10 for fR = 5 GHz with a GS DML at Ibias = 32 mA, fR = 5 GHz, VRF = 1.8 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xiii. 71. 71. 72. 73. 75. 76. 77 79. 80. 81. 82. 84.

(18) 6.13 Simulated optical spectra of a GS laser driven at Ibias = 32 mA, fR = 10 GHz and VRF = 1 V under OI at different Pinj and δν: (a) Pinj = -2 dBm and δν = 16 GHz; (b) Pinj = 2 dBm and δν = 16 GHz, (c) Pinj = 12 dBm and δν = 20 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.1. Temporal traces (upper row) and optical spectra (lower row) of the DML emission under pulsed GS for fixed VRF = 0.9 V and fR = 500 MHz and different values of Ibias . Each column corresponds to the value of Ibias labelled on the top . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Simulated temporal profile of the output power (blue) and carrier density (red) at the same GS conditions as in Fig. 7.1: VRF = 0.9 V and fR = 500 MHz and different values of Ibias . Each column corresponds to the value of Ibias labelled on the top . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Colour maps showing the dependence on VRF and Ibias of the spectral characteristics of the pulses generated by pulsed GS with a PPG at fR = 500 MHz: (a) CNR and (b) ∆f10 . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Temporal trace of the output power (a) and optical spectrum (b) of the light emitted by the laser under 500 MHz pulsed electrical excitation (Ibias = 14.4 mA and VRF = 1.1 V) and OI (Pinj = - 14 dBm, δν = 16 GHz). The injection frequency is indicated by an arrow in (b). 3(c) is a zoom of 3(b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Experimental optical spectra under pulsed GS conditions (Ibias = 14 mA, fR = 500 MHz, VRF = 1.1 V) and different conditions of OI: (a) Pinj = 12 dBm and δν = 9 GHz and (b) Pinj = -24 dBm and δν = - 30 GHz. The injection frequency is indicated with an arrow. . . . . . . . . . . . . . . . 7.6 Colour maps showing the dependence on Pinj and δν of the experimental spectral characteristics at fR = 500 MHz, Ibias = 14 mA, VRF = 1.1 V: (a) CNR; (b) ∆f10 ; and (c) CNR·∆f10 . . . . . . . . . . . . . . . . . . . . . . 7.7 Evolution of the FWHM of the optical pulse ∆t, δf10 and CNR, as a function of the electric pulse width τelec at fR = 500 MHz, IOF F = 12.2 mA, Pinj = - 14 dBm, δν = 16 GHz and different values of ION . The lines are drawn as a guide to the eye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Temporal trace of the output power (a) and optical spectrum (b) of the light emitted by the laser under 100 MHz pulsed electrical excitation, IOF F = 6.5 mA, ION = 156.5 mA and optical injection (Pinj = - 30 dBm, and detuning, δν = 16 GHz). 5(c) is a zoom of 5(b). . . . . . . . . . . . . . . 7.9 Transient behaviour of a SRD: (a) Basic schematic circuit; (b) Transient current response; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.10 (a) Experimental setup for the electrical characterisation of the SRD. Experimental temporal trace (b) and RF spectrum (c) of the electrical pulses generated in SRDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.11 (a) Experimental optical spectrum of the optically-injected GS laser. The driving conditions are: fR = 100 MHz, Ibias = 1.34 mA, VRF −output = 10.5 V, Pinj = -17 dBm, and injection wavelength λinj = 1549.8 nm. The injection frequency is indicated with an arrow; (b) is a zoom of (a) . . . . xiv. . 89. . 90. . 91. . 91. . 92. . 93. . 94. . 95 . 96. . 97. . 97.

(19) 7.12 Simulated optical spectra of the optically-injected GS laser. The driving conditions were: VRF = 3.5 V mA, Ibias = 1 mA, fR = 100 MHz and Pinj = 12 dBm with δν = 50 GHz; (a) Using non-jittered electrical pulses and (b) Using 10-ps jittered electrical pulses . . . . . . . . . . . . . . . . . . . . 98 7.13 (a) Evolution of the electrical timing jitter of the pulses generated by the SRD; (b) Evolution of the optical timing jitter of the generated optical pulses in the externally-injected GS laser for different electrical timing jitter conditions; (c) Experimental optical spectra for the externally-injected GS laser for different electrical timing jitter conditions. . . . . . . . . . . . . . . 99 7.14 Temporal traces (upper row) and optical spectra (lower row) of the DML emission using as pulse source: (a) and (c) the PPG; and (b) and (d) the SRD . The driving conditions were in (a) and (c): fR = 100 MHz, Ibias = 1.7 mA, VRF −output = 7 V and Popt = -27 dBm and λinj = 1550.2 nm; and in (b) and (d): fR = 100 MHz, Ibias = 1.45 mA, VRF −output = 7 V and Popt = -25 dBm and λinj = 1550.195 nm . . . . . . . . . . . . . . . . . . . . . . 100 8.1. 8.2. 8.3. 8.4. 8.5 8.6. 8.7. Schematic diagram of the experimental setup used for heterodyne spectroscopy: ML: master laser; VOA: variable optical attenuator, CW-SL(A): continuous wave slave laser A, GS-SL(B): gain-switched slave laser B; AOM: acousto-optic modulator; DUT: device under test; PD: photodetector, ESA: electrical spectrum analyser . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 (a) Experimental RF spectrum of the beat signal from an OFC generated at 200 MHz from SL(B) and the single tone from the CW-SL(A). Panel (b) is a zoom of panel (a). This measurement was performed in the operation conditions shown in Table 8.1. ESA parameters: RBW = 75 kHz; Average = 10; Sweep time = 30 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Experimental optical spectrum (black) recorded with a BOSA and the reconstructed optical spectrum (blue) from the RF spectrum of the beating between the local oscillator and the OFC under test . . . . . . . . . . . . . 105 Measured RF spectra of the unfiltered (a) and the filtered OFC (b). The OFC for these measurements was generated at the same operation conditions shown in Table 8.1. ESA parameters: RBW = 75 kHz; Average = 10; Sweep time = 6 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Measured (red) and theoretical (blue) transmittance of the tunable FP filter 106 Schematic diagram of the experimental setup used for the characterisation of the HCN gas cell: ML: master laser; VOA: variable optical attenuator, GS-SL(A): gain-switched slave laser A, GS-SL(B): gain-switched slave laser B; AOM: acousto-optic modulator; DUT: device under test; PD: photodetector, ESA: electrical spectrum analyser . . . . . . . . . . . . . . . . . . . . 106 Measured electrical comb a) without gas and b) with gas; (c) Calculated transmittance for the gas cell. The driving and optical conditions of this measurement are summarised in Table 8.2. ESA parameters: RBW = 30 kHz; Average = 10; Sweep time = 0.2 s . . . . . . . . . . . . . . . . . . . . 107. xv.

(20) 8.8. 8.9. 8.10 8.11. 8.12. 8.13. 8.14. Schematic diagram of the experimental setup used for recording the optical spectrum of the H2 S gas cell: ML: master laser; VOA: variable optical attenuator, GS-SL(A): gain-switched slave laser A, GS-SL(B): gain-switched slave laser B; AOM: acousto-optic modulator; OBPF: optical band pass filter, GC: gas cell; PD: photodetector, ESA: electrical spectrum analyser Electrical combs recorded by the ESA when (a) the gas cell is filled only with air (reference) and when (b) it also contains H2 S at 45 mBar; (c) Ratio (blue) and position of the absorption lines extracted from HITRAN database. These measurements were performed in the operation conditions shown in Table 8.3. ESA parameters: RBW = 1 kHz; Average = 30; Sweep time = 6 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of the gated dual-comb architecture according to [118]. Schematic diagram of the experimental setup used for the gated dual-comb experiment: ML: master laser; SL: slave laser; AOM: acousto-optic modulator; SMF: single-mode fiber, EDFA, erbium-doped fiber amplifier, PD: photodetector, ESA: electrical spectrum analyser, OSC: oscilloscope . . . (a) Dual electrical comb spectrum generated under the working conditions summarised in Table 8.4; panel (b) is a zoom of panel (a). The coloured arrows indicate lines corresponding to two overlapped combs. ESA parameters: RBW = 10 kHz; Average = 20; Sweep time = 1.5 s . . . . . . . . . Explanation of the symmetric combs obtained with the gated dual OFCs experiments when the measurement of the signals is performed with the ESA. T1 , first semi-period of the gating cycle; T2 , second semi-period of the 0 gating cycle; frep , repetition frequency to generate the OFC1; frep , repetition frequency to generate the OFC2. The OFC is assumed to be strongly asymmetric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Temporal trace of the measured interferogram for the gated dual-comb configuration in the driving and injection conditions mentioned in Table 8.4; (b) the corresponding electrical spectrum calculated by applying the Fourier transform of the interferogram. Oscilloscope parameters: Sampling Rate = 1.25 GSamples/S; Points = 6250; Average = 10 . . . . . . . . . . . . . . .. xvi. . 108. . 109 . 110. . 111. . 112. . 112. . 113.

(21) List of Tables 4.1 4.2 4.3 4.4. Summary of the experimental techniques used in this thesis and the physical properties and parameters measured through them . . . . . . . . . . . . . Main measured characteristics of the employed lasers . . . . . . . . . . . . The input impedance at low frequency ZL of each laser . . . . . . . . . . . Main parameters of the RF drivers used in all the experiments . . . . . .. 6.1. Summary of main simulation parameters . . . . . . . . . . . . . . . . . . . . 74. 8.1 8.2. Summary of the operation conditions for the heterodyne experiments . . . Summary of the operation conditions for the dual-comb experiments with the gas cell of HCN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of the operation conditions for the dual-comb experiments with the gas cell of H2 S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of the working conditions for the gated dual-comb operation . .. 8.3 8.4. xvii. . . . .. 36 37 40 41. . 103 . 107 . 109 . 111.

(22) xviii.

(23) Chapter 1. Introduction 1.1. Motivation. An optical frequency comb is a group of coherent equally-spaced optical tones. The research in the field of OFC generation began in the 70s. Since then, they are considered as one of the most important advances in photonics during the last century [6]. During the early times of the OFC generation, the OFCs were mostly employed in high-precision spectroscopic measurements. In 2005, John L. Hall and Theodor W. Hänsch were awarded the Nobel Prize in physics for their pioneering and jointly contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique. More recently, the research community has paid special attention to the OFCs as they have opened new possibilities in different fields, such as metrology [7], radio-photonics [8], optical communications [9, 10], molecular spectroscopy [5] and arbitrary waveform generation [11]. Semiconductor lasers have become one of the most important coherent light sources during the last century. The first reports of laser emission from a semiconductor laser were published in 1962, when three different research groups reported coherent emission from a diode laser [12–14]. Since then, these laser sources have become the object of an increasing research effort, coming into the scene for numerous applications. Thanks to their inherent characteristics, they have become one of the most important coherent light sources, representing a significant part of the light source market. Some of the advantages of the semiconductor laser are: • The price of these devices can be very low, reaching the value of less than 5 $ per laser. • The power conversion efficiency of these lasers can reach up to 70 % [15]. • They cover a wide range of wavelengths, going from the ultra-violet to the farinfrared. • The size of these lasers is really small in comparison with other light sources, reaching chip sizes of 1 mm2 . • These lasers can be modulated in a wide range of frequencies up to tens of GHz. • They can be integrated in the well-known Photonic Integrated Circuits (PICs) 1.

(24) Chapter 1 Diode lasers are employed nowadays in many applications, such as CD/DVD players, laser printing, smartphones, medicine, spectroscopy, optical communications, etc... Depending on the application, they can be found with quite different output power levels (from ≤ 100 µW to several kW), emission spectra and type of packaging. Different types of lasers have been employed to generate OFCs depending on the targeted application, such as solid-state lasers [16] and fiber lasers [17]. Semiconductor lasers are also relevant in the generation of OFCs due to their usual credentials, such as high efficiency, low cost and small footprint. There are several strategies for generating OFCs from semiconductor lasers, mode locking, gain-switching, electro-optic modulation, and more recently, micro-ring resonators [18]. GS has attracted specific attention due to its easy implementation, high flexibility in the selection of the repetition frequency and low losses. Although the generation of optical pulses by GS has been extensively studied in the 80s [19–21], only in the past decade, the generation of OFCs by gain-switched semiconductor lasers has become the subject of a relatively high number of application-driven works. The simplicity provided by the GS technique makes much easier the implementation of OFCs generated by semiconductor lasers for specific applications, such as optical communications and spectroscopy. The use of OFCs for spectroscopy is recognized as a simple and useful method to characterise the internal structure of different materials. Recently, much of the attention of the scientific community has been paid to the spectroscopic architecture known as dual-comb spectroscopy. In this technique, two different OFCs with slightly different repetition frequencies are combined in a photo-detector, down-converting the information from optical frequencies into radio frequency (RF), allowing the acquisition with conventional electrical equipment. The employment of this architecture improves the accuracy of the spectroscopic analysis as the measurements can be performed with high-resolution (lower than kHz). Although this scheme is mainly used in molecular spectroscopy, some applications such as Light Detection and Ranging (LIDAR) can also benefit from the implementation of this architecture.. 1.2. Objectives of this thesis. This thesis has been developed in the ”Grupo de Fotónica Aplicada”, which is part of the ”Centro de Materiales y Dispositivos Avanzados para las Tecnologias de la Información y la Comunicación (CEMDATIC)” of the Universidad Politécnica de Madrid (UPM). During the last decades, the members of this research group have focused their research activity into the characterisation and theoretical modelling of several semiconductor lasers. Experimental and theoretical investigation on gain-switching in different types of lasers has been carried out by Consoli et at. [22, 23], during the development of his Ph.D. thesis. In 2013, the group started to work with a special type of two-section laser called MOPA or Master Oscillator Power Amplifier laser, characterising the response of these lasers under direct modulation and gain-switching [24, 25]. The complex dynamics reported in these publications motivated the realisation of an extensive experimental and theoretical investigation of these devices [26–28]. This research activity was performed within the activities of the RANGER and BRITESPACE projects, whose objective was the implementation of two different LIDAR systems for high-precision distance measurements, and atmospheric re2.

(25) Chapter 1 mote carbon dioxide sensing in future Earth observation missions, respectively. The work of this thesis is performed within the activities of the project COMBINA, devoted to study experimental and theoretically the generation of OFCs from gain-switched semiconductor lasers, subject (or not) to optical injection. The fundamental objective of this thesis is to study the generation of OFCs from semiconductor laser by GS, with emphasis in understanding the underlying physics to optimise their performance for different applications. This fundamental goal has been divided into several partial goals: • The determination of the optimal operating conditions to generate OFC with different characteristics, depending on the targeted application. • To acquire a better understanding of the physical phenomena involved in the different comb generation processes, through the development of simulation tools based on a rate equation model, and the comparison of the simulations with the experimental results. • To validate the suitability of the OFCs generated by GS in semiconductor lasers for spectroscopic applications.. 1.3. Structure of this thesis. After this introductory chapter, the thesis is organized as follows: • Chapter 2 ”Fundamentals” presents a summary of the fundamental concepts relevant to this thesis. A brief description of different semiconductor lasers is included. The fundamentals of the OFCs, the central concept of this work, are explained as well as the main techniques used to generate them. Additionally, the heterodyne detection technique and the dual-comb concept is explained in this chapter. • Chapter 3 ”Dynamic response of a semiconductor laser” describes the theoretical model that has been used to simulate the response of the laser. A rate equation model was employed to explain the characteristics of the OFCs in terms of the main physical processes involved in the generation. Special attention has been devoted to the correct mathematical treatment of the stochastic differential equations (SDEs). • Chapter 4 ”Experimental techniques” is devoted to the description of all the components, equipment and measurement techniques used in the experiments, providing the schematics of the employed setups for the characterisation of the lasers and for the OFC generation. Also, schematics of the spectroscopic setups are presented. • The results on the experimental characterisation of the different lasers and OFCs is presented in Chapter 5 ”Optical pulse and frequency comb generation in gain-switched semiconductor lasers”. Power-current-voltage characteristics and optical spectra at different conditions of current and temperature of three different types of lasers are provided. The temporal and spectral characterisation of the OFCs generated by edge-emitting laser diodes under gain-switching and optical injection is detailed. The analysis of the characteristics of the optical pulses generated by GS a 1300 nm vertical-cavity surface-emitting laser is also presented in this chapter. 3.

(26) Chapter 1 • Chapter 6 ”Numerical and experimental analysis of optical frequency comb generation” shows an analysis of the OFC generation in gain-switched semiconductor lasers with and without optical injection through the comparison between experimental and simulated results. The internal parameters of the model were extracted by comparing experimental and simulated relative intensity noise spectra. • A new method to generate low repetition rate high-quality OFCs is presented in Chapter 7 ”OFC generation by pulsed gain-switching and optical injection”. An experimental study on the characteristics of the OFC generated by pulse excitation and OI is presented, employing two different pulsing sources: a pulse pattern generator (PPG) and a step-recovery diode. In the latter, special attention is devoted to the effect of the source timing jitter on the characteristics of the generated OFCs. • Chapter 8 ”Spectroscopic applications of optical frequency combs” presents some spectroscopic applications of the OFC generated in externally-injected gainswitched semiconductor lasers. Different techniques, such as the heterodyne detection and the dual-comb spectroscopy, are employed to determine with high resolution the transmittance of a tunable Fabry-Perot (FP) filter and the absorption spectra of two different gas species. • Chapter 9 ”Conclusions and future work” summarises the conclusions and future research lines of the thesis. Finally, the contributions of the author to journal articles and conferences resulting from this work can be found in the Appendix A.. 4.

(27) Chapter 2. Fundamentals Introduction The fundamentals of semiconductor lasers are introduced in this chapter. Section 2.1 presents general and intuitive ideas about the lasing condition in a resonant cavity, considering a FP cavity. A summary of the main characteristics of the FP lasers is shown in this section. Section 2.2 presents the fundamentals of the main technique for the generation of optical pulses in semiconductor lasers employed in this thesis, the gain-switching. The basis of the optical injection are explained and discussed in Section 2.3. Section 2.4 is devoted to the concept of the optical frequency comb within this section. A historical revision of the development of the OFCs is presented in Section 2.4.1. The principle of operation of the OFCs is explained in Section 2.4.2. Then, some techniques for OFC generation from semiconductor lasers, such as mode-locking or electro-optic modulation are described and their basic characteristics are discussed in Section 2.4.3. Finally, in Section 2.5 the fundamentals of homodyne and heterodyne detection, as well as the principle of operation of the dual-comb spectroscopy are described.. 2.1 2.1.1. Semiconductor lasers Basic structure: Fabry-Perot laser. Fig. 2.1(a) shows the schematics of a typical FP laser diode, which is based on a p-n junction and a FP cavity. The active medium is sandwiched between a p and an n-doped cladding layers. The stimulated emission is produced by the recombination between the electrons and the holes of the conduction and valence band, respectively (Fig. 2.1(b)). When the laser is unbiased, there are no carriers in the active layer. As long as the current applied to the laser is increased, the number of carriers in the active material increases as well and the material reaches transparency. At higher injection currents, the material is in positive optical gain conditions. However, optical gain is not the only condition to generate laser emission. The other key point of the process is the optical feedback, which is provided by the resonant cavity, i.e, the FP cavity. The FP cavity consists of the own facets of the device that are perfectly cleaved along the crystallographic planes. The reader can find more information about semiconductor laser physics in [29, 30]. The optical field inside the FP cavity can be decomposed in two overlapped and op5.

(28) Chapter 2. Ec Metal contact P-material. Ca v Wi ity dth. e-. Active region. E h+. N-material. Ev. Cavity Length. (a). (b). Figure 2.1: (a) Schematics of a FP laser diode. (b) Band diagram of the conduction and valence bands in a single quantum-well laser posite fields (E + and E − ) propagating along the longitudinal direction (Fig. 2.2): E(z, ω) = E + e−j β̄z + E − ej β̄z. (2.1). where β̄ is the complex propagation constant given by: j β̄ = β + (gm − αin ) 2. (2.2). In Eq. 2.2, β = 2πnef f /λ where nef f is the effective refractive index, λ is the wavelength in vacuum, gm is the modal gain and αin is the internal loss coefficient, arising from scattering and free carrier absorption. The boundary conditions at each facet of the cavity,. R1. R2. Cavity length E+. Active medium. Ez=0. z=L. Figure 2.2: Schematics of a FP cavity (z = 0 and z = L) impose the round-trip condition needed for the laser oscillation, i.e, the optical field does not change after a round-trip along the cavity. The first relationship provided by this condition determines the relation between the modal gain at threshold and the losses: gm |th = αin + αm (2.3) According to Eq. (2.3), the threshold condition for the laser operation is fulfilled when the modal gain is equal to the cavity losses, given by the addition of the internal losses (αin ) and the mirror losses (αm = L1 ln( √R1 R ) where R1 , R2 are the reflectivities of the 1 2 two mirrors). Although spontaneous emission of photons appears when the semiconductor laser is biased, Eq. (2.3) is only satisfied at the threshold condition, which is reached when 6.

(29) Chapter 2 the laser is driven at the threshold current (Ith ). Below this current, the laser emits only incoherent light with low output power. However, above Ith , Eq. (2.3) is satisfied and the light emitted from the laser is predominantly coherent, following a linear evolution with the bias current. Fig. 2.3(a) presents an experimental power-current (P-I) characteristic of a commercial semiconductor laser, illustrating this effect. Modal. Power (mW). 10 8 6 4 2 0. 0. 20 40 60 80 Current (mA). Figure 2.3: (a) Measured power-current curve of a commercial discrete mode laser (Ith = 14.5 mA). More details about the experimental device are provided in Chapter 4. (b) Gain spectra and cavity losses together with the wavelengths of the longitudinal modes of the cavity (extracted from [1]) The second relationship arising from the round-trip condition is related to the real part of the propagation constant: 2βL = 2mπ (2.4) where m = 1, 2, 3, ... is an integer corresponding to the mode number. Then, the frequency of each mode is given by: mc , (2.5) fm = 2Lnef f where c is the light speed. Therefore, the wavelength of each mode is: λm =. 2Lnef f m. (2.6). Fig. 2.3(b) shows the gain spectra, the cavity losses and the cavity modes in a FP laser. When the carrier density increases, the amplitude and width of the gain spectrum increases as well, until the gain of one of the longitudinal modes reaches the threshold condition. Therefore, when the laser is biased above threshold, the FP mode closest to the gain peak starts lasing. As the difference in the gain for the longitudinal modes is very small, there is mode hopping, and several modes appear in the measured spectra. An example of the emission of a FP laser is depicted in Fig. 2.4 (notice the logarithmic scale).. 2.1.2. Single frequency semiconductor lasers. Semiconductor lasers can be classified as single longitudinal mode (SLM) or multi-longitudinal mode (MLM). The side-mode suppression ratio (SMSR) establishes the criteria to determine this characteristic. The SMSR is defined as the difference (in dB) between the amplitude of the main emitting mode and the amplitude of the highest side mode. A 7.

(30) Chapter 2. Power (dBm). 0 -20 -40 -60 -80. 1535. 1545 1555 Wavelength (nm). 1565. Figure 2.4: Measured optical spectrum of a commercial FP laser (Roithner LFO-18-ip) at I = 45 mA (Ith = 8 mA). This figure was extracted from [1] laser with a SMSR higher than 30 dB is considered as SLM. Different approaches have been followed to achieve single-frequency emission. A wavelength discriminator structure is required to select a single longitudinal mode, either by enhancing the gain of that longitudinal mode or by increasing the losses of the other modes of the cavity. Some approaches for single-frequency operation are described in the following section.. Reflected Power. Distributed Bragg reflector and distributed feedback lasers. (a). n1. n2 Λ. (b). -10 -5 0 5 10 (β - βB)L. Figure 2.5: (a) Schematic of a Bragg grating structure: a periodic array of alternating regions with different indices n1 and n2 with a period Λ; (b) Reflected power as a function of β A Bragg grating is a structure with a periodically varying refractive index (Fig. 2.5(a)). These structures can achieve high reflectivities (Fig. 2.5(b)) at the Bragg wavelength λBragg , given by: λBragg = 2nef f Λ (2.7) An example of the reflectivity of a Bragg grating has been plotted in Fig. 2.5(b) as a function of the detuning between the propagation constant of the incident light (β) and the propagation constant corresponding to the Bragg wavelength. As it can be seen in this figure, the reflectivity of the Bragg grating is maximum for the Bragg wavelength. The Bragg grating technology has been employed to develop high-reflective mirrors to confine efficiently the light inside optical cavities. The distributed Bragg reflector (DBR) lasers are based on this technology. The reflectivity of the longitudinal modes 8.

(31) Chapter 2 whose frequencies are close to the maximum is high, whereas the reflectivity is low for those frequencies outside of this region. The typical structure of a DBR laser is shown in Fig. 2.6. The DBR are the mirrors of the cavity. The Bragg gratings act as highDBR P-material DBR Active region. Ca v Wi ity dth. N-material. Cavity Length. Figure 2.6: Schematic of a DBR laser reflectivity narrowband mirrors, and therefore, they provide a high reflectivity for one of the cavity modes. Thus, the mirror losses for that particular mode are lower than for the others, resulting in SLM operation. If the Bragg grating is extended over the whole cavity and it is acting as the feedback mechanism of the laser, the device is called distributed feedback laser. The typical structure of a DFB laser is shown in Fig. 2.7(a). As it can be seen in the figure, the Metal contact P-material. 0 HR Coating. Active region. Ca v Wi ity dth. N-material. PSD (dBm). AR Coating. -20. (b). -40 -60 -80. Cavity Length. 1547. (a). 1548 1549 1550 Wavelength (nm). 1551. Figure 2.7: (a) Schematic of a DFB laser; (b) Measured optical spectrum of a DFB at Ibias = 25 mA. More details of this laser are provided in Chapter 4. Bragg grating is fabricated in such a way that the index changes periodically along the longitudinal direction of the device. These lasers select, in principle, two different longitudinal modes. However, different approaches, such as the use of an anti-reflection coating in the front facet and a high-reflection coating in the back facet, allow the change from bi-mode to single-mode emission. Fig. 2.7(b) presents the measured optical spectrum of a commercial DFB laser. The laser exhibits a SMSR larger than 45 dB. In this spectrum, the emission linewidth is expected to be lower than 1 MHz. However, as the resolution of the employed optical spectrum analyser (OSA) is much higher (6.25 GHz), the apparent linewidth is given by the OSA filter.. 9.

(32) Chapter 2 Discrete mode lasers The discrete mode laser is a type of egde-emitting SLM laser that was recently developed by the Dublin City University (DCU) and Eblana Photonics [2, 31]. The DML technology is based on the classic FP architecture. However, single-mode operation is achieved by introducing several perturbations of the refractive index in the ridge waveguide. A schematic view of a DML is presented in Fig. 2.8. Using this approach, the multiple longitudinal modes characteristic of a FP cavity are almost suppressed, enhancing just a single longitudinal mode of the cavity. High SMSRs can be achieved using this technology.. Etched features. Ridge Waveguide. Active Material. Active Material. Substrate. Substrate. Side view. End view. Figure 2.8: Schematic view of the DML structure. Top: SEM image of the etched feature pattern. Figure extracted from [2]. PSD (dBm). It is important to mention that the etched waveguide is not working as in an usual DFB. In this case, the etched features are used as the wavelength selector and not as the primary source of optical feedback. The spacing, the depth and the slot number are key parameters to operate these devices as SLM. An example of the optical spectrum of a commercial DML is provided in Fig. 2.9. As it can be clearly seen in this figure, although. -20 -40 -60 1530. 1540. 1550 1560 Wavelength (nm). 1570. Figure 2.9: Measured optical spectrum of a DML at Ibias = 25 mA. More details of this laser are provided in Chapter 4.. 10.

(33) Chapter 2 the modes of the FP cavity are present in the spectrum, all of them are highly suppressed (SMSR > 30 dB) in comparison with the main emitting mode. Vertical-cavity surface-emitting lasers The vertical-cavity surface-emitting lasers (VCSELs) are laser diodes in which the resonant cavity is perpendicular to the active layer. The light in these devices is emitted from the top or from bottom in contrast to the edge-emitting lasers (such as DFB or DML). A schematics of a VCSEL is shown in Fig 2.10. The active region is sandwiched between. DBR-A. Active region. DBR - B Figure 2.10: Schematic representation of a VCSEL two DBRs. The combined effect of the high frequency separation between longitudinal modes (due to the small size of the cavity) and the optical bandwidth of the gain selects a single longitudinal mode. Due to the small size of the cavity, the modal gain is low. For this reason, the mirrors of the cavity are high-reflectivity DBRs. This reduces the mirror losses, confining the light within the cavity. The output power of a VCSEL is usually low but the low energy consumption and the threshold current are also low.. PSD (dBm). 0 -20. (a). (b). -40 -60 -80 1310 1312 1314 1316 1312.2 1312.6 1313 Wavelength (nm) Wavelength (nm). Figure 2.11: (a) Measured optical spectrum of a 1300 nm VCSEL. Panel (b) is a zoom of (a). More details of this device can be found in Chapter 4. An example of the optical spectrum of a commercial VCSEL is presented in Fig 2.11. As it can be clearly seen in Fig 2.11(a), the amplitude of the main emitting mode is several orders of magnitude higher than the side modes (SMSR = 57 dB). Although it cannot be seen in Fig 2.11(b), due to the limited resolution of the OSA, an additional orthogonally polarised mode with lower amplitude is expected in the optical spectrum. An in-depth analysis of these devices can be found in [32, 33].. 11.

(34) Chapter 2. 2.2. Gain-switching. 0. 2.5 1.8 2.2 Time (ns). 2. Power (mW). 10. N=Nth. 3. 20 10 0. 3.5. (b). N<Nth 3 N>Nth 1.85 1.95 Time (ns). 2.5 2. Carrier density (Ntr). 20. 3.5. (a). Carrier density (Ntr). Power (mW). Optical pulse generation in semiconductor lasers can be achieved by multiple techniques. One of the simplest techniques is gain-switching. This technique has been extensively used to generate narrow optical pulses from semiconductor lasers [20, 22, 34, 35]. The antecedents of this technique will be reviewed in Chapter 5.. Figure 2.12: (a) Result of simulations of the current (black), carrier density (red) and photon density (blue) during the turn-on process; (b) Enlarged view during the first spike of the relaxation oscillations In order to understand the underlying physics behind GS, it is necessary to describe the switch-on process. Fig. 2.12 shows the results of a numerical simulation of the behaviour of the current, carrier and photon density during the turn-on of the laser. The equations will be described in Chapter 3. The applied current is current step, i.e, the total current is I(t) = Iof f + Ion ∆rect(t), where Iof f is the low level of the current, Ion is the amplitude of the step signal and rect(t) is an instantaneous step increment. If a step current from below to above threshold is applied, the carrier density increases less abruptly, and at given time, it equals its threshold value (dotted line in Fig. 2.12). The output power starts increasing at this point. Later, when the stimulated recombination rate is high enough, the carrier density starts decreasing as the carriers are depleted by stimulated recombination, and the optical pulse is almost extinguished. However, as the applied current is above threshold, the carrier density increases again, yielding an oscillatory process until the steady state is reached. During this transient process, both the carrier density and the output power oscillate. These oscillations are called relaxation oscillations. The standard gain-switching approach in semiconductor lasers consists in driving the laser with a superposition of two different types of signals: a bias current and a microwave/RF signal, generally with a sinusoidal profile [3, 34]. A representation of this process is shown in Fig. 2.13. When the laser is biased close to Ith and it is modulated by a RF signal with a large amplitude, it is possible to generate narrow optical pulses, as the carrier density is being drastically modulated below and above threshold. The idea underlying this technique is exciting the laser only during the time of the initial peak, suppressing the electrical excitation during the relaxation oscillations [36]. This can be easily obtained when the period of the driving current is short, i.e, for high frequency. The reader can find more information about pulse generation by GS in semiconductor lasers in [36, 37]. 12.

(35) 3.5. 15. 3. 10. 2.5. 5 0. 0. 0.2 0.4 Time (ns). 2 0.6. Carrier density (Ntr). Power (mW). Chapter 2. Figure 2.13: Results of simulations at 5 GHz of the current (black), carrier density (red) and photon density (blue) in GS operation. 2.3. Optical injection. External optical injection in semiconductor lasers has attracted a lot of attention in the last decades, as it is a method to improve the quality of the emission using a simple and flexible scheme [38–41]. OI consists of injecting external light from a laser, which is called master laser (ML), in the cavity of another laser (commonly known as slave laser or SL). The effect of the injection causes a change in the internal field of the slave laser, giving rise to different emission regimes. This configuration can be implemented via free-space optics with lenses, or by using a fiber-based circuit where the two involved lasers are connected by an optical circulator. A schematic diagram of the fiber based approach is presented in Fig. 2.14.. ML. SL Figure 2.14: Schematics of the configuration for the OI of a laser diode: ML: master laser, SL: slave laser The OI system can be described by two primary parameters: the injected power (Pinj ) into the SL and the detuning (δν = νM L − νSL ) between the injected tone and the nominal frequency of the laser in free-running regime. In the ideal OI conditions, i.e., the emission wavelength of the SL is pulled towards the ML wavelength and the SL emission inherits the same characteristics of the ML, such as the phase noise. This transference process is called injection locking. More information about this technique is provided in [42]. Some features of the laser emission, such as the modulation response [43–45], the phase noise [46, 47] and the emission linewidth [3] can be improved using OI. Fig. 2.15(a) shows an example of the linewidth reduction due to the OI. In the example 13.

(36) -80. (a). -90. W/O OI. RIN (dB/Hz). Power (dBm). Chapter 2. -100 -110 -120 -20. -10 0 10 Frequency (MHz). 20. -120. (b). W/O OI. -140 -160 -180 0.1 1 10 Frequency (MHz). Figure 2.15: (a) Measured RF spectra of the delayed self-heterodyne signal of a DFB laser for Ibias = 30 mA without (blue) and with OI (red). More details are provided in Chapter 5. (b) Simulated RIN spectra for Ibias = 20 mA without (blue) and with OI (red); external light is injected with Pinj = 12 dBm and δν = 5.4 GHz the measured linewidth of the DFB decreases from 600 to 70 kHz after being injected. More details can be found in Chapter 5. The linewidth was measured using the technique called delayed self-heterodyne (DSH), described in Section 2.5. The simulated RIN spectra of a laser is illustrated in Fig. 2.15(b) without and with injection. These simulations have been performed using the model described in Chapter 3. The reader can find more information about this topic in Chapters 3 and 6. As it is illustrated in Fig. 2.15(b), the use of this technique leads to an increase of the relaxation oscillation frequency, and hence the modulation bandwidth [40]. The effect of OI in semiconductor lasers operated in CW regime has been extensively analysed, paying special attention to the non-linear dynamic regimes that can be induced [40, 48]. Examples of these dynamics are self-pulsations, four-wave mixing and chaotic behaviour.. 2.4 2.4.1. Optical frequency combs Introduction. An optical frequency comb consists of an equally spaced group of optical tones (also known as lines, peaks or carriers). These optical tones are coherent, i.e, they are highly phase correlated. In general terms, an ideal OFC arises from a train of narrow coherent pulses whose correspondence in the frequency domain by means of the Fourier transform is a group of mutually coherent optical carriers. The origin of the OFCs can be attributed to the investigation in this field of the research group of Theodor W. Hänsch by the end of the 70s. OFC generation was initially associated to mode-locked lasers, as the first results in OFC generation were obtained by his group in 1977 [49] in mode-locked femtosecond dye lasers. This research group has become the spearhead in OFC generation demonstrating that stable optical pulses, equally spaced in time and generated by a mode-locked laser represent a group of tones equally spaced in the spectral domain. Since this major breakthrough, OFCs generated by modelocked lasers were mostly employed in high-precision spectroscopic measurements. In the meantime, the photonic community efforts led to develop ultrafast lasers, improving the. 14.

(37) Chapter 2 stability and decreasing the pulse width of the optical pulses [50], until the first Ti:Sapphire lasers appeared at the 80s decade. These lasers were capable of generating femtosecond optical pulses. Since the commercialisation of these devices, the generation of ultra-short optical pulses became more affordable and feasible, allowing the use of ultrafast lasers for OFC generation. Udem et al. [51] proved the viability of using a femtosecond-laser as a frequency comb synthesizer, reporting OFC generation in mode-locked lasers with a bandwidth of 20 THz. The first absolute frequency measurement was performed in 2000 [52], using a mode-locked based OFC. Comparing with the Cesium clock of the Bureau National de Metrologie, Niering et. al reported for the first time the precise and accurate measurement of the frequency of the two-photon 1S-2S resonance with an uncertainty of 1.9 × 10−14 , improving the accuracy previously achieved by any other optical measurement. This event is considered as the first experiment in high-precision metrology using an OFC. John L. Hall and Theodor W. Hänsch were awarded in 2005 with the Nobel Prize in physics for their pioneering and jointly contributions on OFCs for spectroscopic applications. In recent years, the use of OFCs has spread in other photonic fields. Although the first results in OFC generation were obtained with mode-locked lasers, now several methods can be used to obtain high-quality OFCs at different frequencies. Although high-resolution metrology [7] was initially the main application of the OFCs, during the recent decades OFCs have found application in other photonics fields. RF photonics [8] and optical communications [9,10] have become areas of interest for the generation of OFCs at high frequencies. More recently, the OFG generation at low frequencies has attracted special attention for spectroscopic applications, specially the dual-comb architecture [53–55].. 2.4.2. Comb operation. An ideal OFC can be equivalently described in the time domain as a train of periodic and coherent optical pulses and in the spectral domain as a series of equally spaced spectral components which intensity profile is related with the pulse shape. The relationship between the two pictures is given by the Fourier transform. Fig. 2.16 shows schematically the correspondence between the two descriptions. In the frequency domain, the frequency of each tone fn can be expressed as: fn = f0 + nfr ,. (2.8). where fr is the frequency separation, i.e., the repetition rate of the pulse train, and f0 is the carrier envelope frequency offset. Consistently with the duality of this ideal description, the spectral width of the OFC is just the reciprocal of the pulse width. The carrier envelope frequency offset, f0 is due to the difference between the phase and group velocity. Though not relevant for the objectives of this thesis, its determination has been very important for applications requiring the accurate knowledge of the absolute value of the frequency. Several methods [16, 56–58] have been used for finding it. The best-known is the f-2f self-referencing method [56]. When the optical spectrum is broader than an octave in frequency, i.e, the highest frequency of the OFC is twice the value of the lowest one, the self-referencing method is greatly simplified. It consists of filtering one line 15.